Competing single-particle and collective states in the low-energy structure of ${}^{113}$I

To understand the low-energy structure of the neutron deficient iodine isotopes, lifetimes for the low-lying $9/2^{+}$ and $11/2^{+}$ positive-parity states in ${}^{113}$I have been measured as $\tau =28\left(4\right)$ ps and $\tau =3.7\left(7\right)$ ps, respectively. The lifetime for the $11/2^{-}$ state, which feeds the $9/2^{+}$ and $11/2^{+}$ states, was remeasured with improved accuracy as $\tau =216\left(7\right)$ ps. The reduced transition probability, $B\left(E2\right)=32\left(5\right)$ W.u., for the $9/2^{+}\to 5/2^{+}$ transition agrees with that calculated within the shell model using a Hamiltonian based on the charge-dependent Bonn nucleon-nucleon interaction. In contrast, the much larger transition probability, $B\left(E2\right)=209\left(39\right)$ W.u., measured for the $11/2^{+}\to 7/2^{+}$ transition has been interpreted, with the aid of configuration-constrained total Routhian surface calculations, as resulting from a slightly $\gamma$-soft rotor with an associated quadrupole deformation of ${\beta }_2\approx 0.18$. Remarkably similar reduced $E1$ transition probabilities of $5.5\left(5\right)\times {10}^{-4}$ and $4.9\left(5\right)\times {10}^{-4}$ W.u. were deduced for the $11/2^{-}\to 9/2^{+}$ and $11/2^{-}\to 11/2^{+}$ transitions, respectively, which feed apparently dissimilar but competing structures.

Figure 1

$\gamma$-ray spectra obtained from a Jurogam-II clover vs clover $\gamma$-$\gamma$ matrix. (a) Total (ungated) projection with the energies of the ${}^{113}$I transitions that are of particular relevance to this work highlighted. Transitions marked with symbols originate from nuclei produced in reactions on the target (${}^{114}$Xe) and Mg degrader foil ($A\sim 80$). (b) 531 keV gated spectrum with ${}^{113}$I transitions labeled with their energy.

Figure 2

Partial level scheme for ${}^{113}$I, produced from a $\gamma$-$\gamma$ correlation matrix, showing the states and transitions that are of particular importance in this work. The observed correlations confirm the transition ordering reported in Refs. [9, 10]. The state lifetimes shown are those measured in this work.

Figure 3

638 keV (ring 2) gated spectra, recorded by the Jurogam-II ring 1 ($\theta ={157}^{\circ }$) detectors, showing the shifted (left peak) and degraded (right peak) components of the 531 keV transition, from the $15/2^{-}$ state for target-to-degrader distances of (a) 61.7, (b) 216.6, (c) 329.2, and (d) 759.8 $\mu$m. Gaussian fits used to extract the component intensities are also shown (dashed and solid lines).

Figure 4

(a) The lifetime of the 11/2${}^{-}$ state evaluated for each target-degrader separation in the region-of-sensitivity along with the weighted mean of 216 ps (solid line) and its uncertainty $\pm$7 ps (dashed lines). (b) Normalized shifted intensities for the $11/2^{-}\to 9/2^{+}$ 388 keV decay along with the results of a least-squares fit (solid line).

Figure 5

864 keV (ring 2) gated spectra, recorded by the Jurogam-II ring 1 ($\theta ={157}^{\circ }$) detectors, showing the shifted (left peak) and degraded (right peak) components of the 690 keV transition, from the $11/2^{+}$ state in ${}^{113}$I, for target-to-degrader distances of (a) 7.6, (b) 100.3, and (c) 9976 $\mu$m. Gaussian fits used to extract the component intensities are also shown (dashed and solid lines).

Figure 6

(a) The lifetime of the 11/2${}^{+}$ state evaluated for each target-degrader separation in the region-of-sensitivity along with the weighted mean of 3.7 ps (solid line) and its uncertainty $\pm$0.7 ps (dashed lines). (b) Normalized shifted intensities for the $11/2^{+}\to 7/2^{+}$ 690 keV decay along with the results of a least-squares fit (solid line).

Figure 7

629 keV (ring 2) degraded component gated spectra, recorded by the Jurogam-II ring 1 ($\theta ={157}^{\circ }$) detectors, showing the shifted (left peak) and degraded (right peak) components of the 388 keV transition, feeding the $9/2^{+}$ state, for target-to-degrader distances of (a) 216.6, (b) 2603, and (c) 9976 $\mu$m. Gaussian fits used to extract the component intensities are also shown (dashed and solid lines).

Figure 8

(a) The lifetime of the 9/2${}^{+}$ state evaluated for each target-degrader separation in the region-of-sensitivity along with the weighted mean of 28 ps (solid line) and its uncertainty $\pm$4 ps (dashed lines). (b) Normalized shifted intensities for the $11/2^{-}\to 9/2^{+}$ 388 keV decay along with the results of a least-squares fit (solid line).

Figure 9

Comparison between the experimentally determined level energies for the low-lying positive-parity states and those calculated within the framework of the shell model. Calculations were performed with the code nushell@msu [21] utilizing the ‘sn100pn’ Hamiltonian [22] with an effective interaction derived from the CD-Bonn nucleon-nucleon potential [1, 23].

Figure 10

Graphical representation of the shell-model calculated wave functions for the low-lying excited 9/2${}^{+}$, 7/2${}^{+}$, and 11/2${}^{+}$ states in ${}^{113}$I. The bottom (blue with no pattern), middle (red with horizontal lines), and top (green with vertical lines) portions of each bar denote the $\pi g_{7/2}^2{d}_{5/2}^1$, $\pi g_{7/2}^1{d}_{5/2}^2$, and $\pi g_{7/2}^3$ contributions, respectively.

Figure 11

Results from configuration-constrained total Routhian surface calculations for the $11/2^{+}$ state in ${}^{113}$I. The calculated surface shows a minimum at ${\beta }_2=0.18$, $\gamma =7.4^{\circ }$ for the $11/2^{+}$ state at an excitation energy of 690 keV with a configuration of $1/2^{+}\left[420\right]$.